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Numerical Analysis and Computation Commons™
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- Continuity (1)
- Eigenvalue problem (1)
- Error bounds (1)
- Finite element method on surfaces (1)
- Generalized Purcell method (1)
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- Generalized Purcell minimal residual method (1)
- Ill-conditioned problems (1)
- Krylov subspace methods (1)
- Laplace-Beltrami operator (1)
- Linear operator (1)
- Matrix dilation (1)
- Matrix translation (1)
- Model (1)
- Multiwavelet frame (1)
- Over fitting (1)
- Regularization (1)
- Subdivision scheme (1)
- Wavelet (1)
- Weighted minimal residual method (1)
Articles 1 - 4 of 4
Full-Text Articles in Numerical Analysis and Computation
Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer
Projected Surface Finite Elements For Elliptic Equations, Necibe Tuncer
Applications and Applied Mathematics: An International Journal (AAM)
In this article, we define a new finite element method for numerically approximating solutions of elliptic partial differential equations defined on “arbitrary” smooth surfaces S in RN+1. By “arbitrary” smooth surfaces, we mean surfaces that can be implicitly represented as level sets of smooth functions. The key idea is to first approximate the surface S by a polyhedral surface Sh, which is a union of planar triangles whose vertices lie on S; then to project Sh onto S. With this method, we can also approximate the eigenvalues and eigenfunctions of th Laplace-Beltrami operator on these “arbitrary” surfaces.
Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal
Stability Of Multiwavelet Frames With Different Matrix Dilations And Matrix Translations, F. A. Shah, Sunita Goyal
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study the stability of multiwavelet frames with different matrix dilations and matrix translations by means of operator theory and show that these frames remain stable over some kinds of perturbations of the basic generators.
A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam
A Subdivision-Regularization Framework For Preventing Over Fitting Of Data By A Model, Ghulam Mustafa, Abdul Ghaffar, Muhammad Aslam
Applications and Applied Mathematics: An International Journal (AAM)
First, we explore the properties of families of odd-point odd-ary parametric approximating subdivision schemes. Then we fine-tune the parameters involved in the family of schemes to maximize the smoothness of the limit curve and error bounds for the distance between the limit curve and the kth level control polygon. After that, we present the subdivision-regularization framework for preventing over fitting of data by model. Demonstration shows that the proposed unified frame work can work well for both noise removal and overfitting prevention in subdivision as well as regularization.
A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh
A New Implementation Of Gmres Using Generalized Purcell Method, Morteza Rahmani, Sayed H. Momeni-Masuleh
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, a new method based on the generalized Purcell method is proposed to solve the usual least-squares problem arising in the GMRES method. The theoretical aspects and computational results of the method are provided. For the popular iterative method GMRES, the decomposition matrices of the Hessenberg matrix is obtained by using a simple recursive relation instead of Givens rotations. The other advantages of the proposed method are low computational cost and no need for orthogonal decomposition of the Hessenberg matrix or pivoting. The comparisons for ill-conditioned sparse standard matrices are made. They show a good agreement with available …